Problem: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = 3$ $a_i = a_{i-1} - 6$ What is $a_{13}$, the thirteenth term in the sequence?
From the given formula, we can see that the first term of the sequence is $3$ and the common difference is $-6$ To find the thirteenth term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = 3 - 6(i - 1)$ To find $a_{13}$ , we can simply substitute $i = 13$ into the our formula. Therefore, the thirteenth term is equal to $a_{13} = 3 - 6 (13 - 1) = -69$.